Deterministic Preparation Research Articles

Deterministic Preparation of a Hyper‐Entangled Three‐Photon Asymmetric W State Assisted by the Single‐Sided QD‐Cavity System

AbstractHyper‐entangled states that encode qubits in multiple degrees of freedom of a quantum system can provide a decisive advantage in quantum information processing, such as improving the capacity of communication and speeding up the computation. Assisted by quantum dots in single‐sided optical microcavities, nonlinear interaction of optical circular polarizations is induced and a deterministic scheme for preparing a three‐photon hyper‐entangled asymmetric W state with polarization degree of freedom and spatial degree of freedom is proposed. The preparing process is composed of three steps: the preparation of a three‐photon polarization entangled asymmetric W state; the preparation of a three‐photon spatial entangled asymmetric W state; the preparation of a three‐photon hyper‐entangled asymmetric W state. It can be generalized to generate a three‐photon general W state according to practical requirement.

Deterministic preparation of supersinglets with collective spin projections

We introduce a procedure to generate supersinglets, the multipartite generalization of angular momentum singlet states. A supersinglet is defined as a total spin zero state consisting of $N$ spin-$j$ particles. They are highly entangled and have zero spin variance in any direction, and as such are potentially useful for quantum metrology. Our scheme is based on projective measurements that measure the collective spin of the whole spin ensemble. A local unitary rotation is applied conditionally on the measurement outcome, such as to maximize the probability of obtaining spin zero on the subsequent measurement. The sequence is repeated in the $z$ and $x$ basis until convergence is obtained towards the supersinglet state. Our sequence works regardless of the initial state, and no postselection is required. Due to the use of strong projective measurements, very fast convergence towards zero spin variance is obtained. We discuss an example implementation using quantum nondemolition measurements in atomic ensembles, and perform numerical simulations to demonstrate the procedure.

Efficient deterministic preparation of quantum states using decision diagrams

Loading classical data into quantum registers is one of the most important primitives of quantum computing. While the complexity of preparing a generic quantum state is exponential in the number of qubits, in many practical tasks the state to prepare has a certain structure that allows for faster preparation. In this paper, we consider quantum states that can be efficiently represented by (reduced) decision diagrams, a versatile data structure for the representation and analysis of Boolean functions. We design an algorithm that utilizes the structure of decision diagrams to prepare their associated quantum states. Our algorithm has a circuit complexity that is linear in the number of paths in the decision diagram. Numerical experiments show that our algorithm reduces the circuit complexity by up to 31.85% compared to the state-of-the-art algorithm, when preparing generic $n$-qubit states with ${n}^{3}$ nonzero amplitudes. Additionally, for states with sparse decision diagrams, including the initial state of the quantum Byzantine agreement protocol, our algorithm reduces the number of controlled-nots by 86.61--99.9%.

Deterministic Remote Preparation of an Arbitrary Single-Qudit State with High-Dimensional Spatial-Mode Entanglement via Linear-Optical Elements

Deterministic Remote Preparation of an Arbitrary Single-Qudit State with High-Dimensional Spatial-Mode Entanglement via Linear-Optical Elements

Dissipation-enabled resonant adiabatic quantum state transfer: Entanglement generation and quantum cloning

Resonant dissipation-enabled adiabatic quantum state transfer processes between the polarization degrees of freedom of a single photon wave packet and quantum emitters are discussed. These investigations generalize previous work [N. Trautmann and G. Alber, Phys. Rev. A 93, 053807 (2015)] by taking into account the properties of the spontaneously emitted photon wave packet and of non adiabatic corrections. It is demonstrated that the photonic degrees of freedoms of these adiabatic one-photon quantum state transfer processes can be used for the passive, heralded and deterministic preparation of Bell states of two material quantum emitters and for realizing a large family of symmetric and asymmetric quantum cloning processes. Although these theoretical investigations concentrate on waveguide scenarios they are expected to be relevant also for other scenarios as long as the processes involved are adiabatic so that the Fourier-limited bandwidth of the single photon wave packet involved is small in comparison with the relevant dissipative rates.

Deterministic remote state preparation of arbitrary three-qubit state through noisy cluster-GHZ channel

We propose a novel scheme for remote state preparation of an arbitrary three-qubit state with unit success probability, utilizing a nine-qubit cluster-GHZ state without introducing auxiliary qubits. Furthermore, we proceed to investigate the effects of different quantum noises (e.g., amplitude-damping, phase-damping, bit-flip and phase-flip noises) on the systems. The fidelity results of three-qubit target state are presented, which are usually used to illustrate how close the output state is to the target state. To compare the different effects between the four common types of quantum noises, the fidelities under one specific identical target state are also calculated and discussed. It is found that the fidelity of the phase-flip noisy channel drops the fastest through the four types of noisy channels, while the fidelity is found to always maintain at 1 in bit-flip noisy channel.

Heralded preparation of spin qubits in droplet-etched GaAs quantum dots using quasiresonant excitation

We present a first comprehensive study on deterministic spin preparation employing excited state resonances of droplet etched GaAs quantum dots. This achievement facilitates future investigations of spin qubit based quantum memories using the GaAs quantum dot material platform. By observation of excitation spectra for a range of fundamental excitonic transitions the properties of different quantum dot energy levels, i.e. shells, are revealed. The innovative use of polarization resolved excitation and detection in quasi-resonant excitation spectroscopy facilitates determination of $85$ $\%$ maximum spin preparation fidelity - irrespective of the relative orientations of lab and quantum dot polarization eigenbases. Additionally, the characteristic non-radiative decay time is investigated as a function of ground state, excitation resonance and excitation power level, yielding decay times as low as $29$ ps for s-p-shell exited state transitions. Finally, by time resolved correlation spectroscopy it is demonstrated that the employed excitation scheme has a significant impact on the electronic environment of quantum dot transitions thereby influencing its charge and coherence.

Deterministic preparation of nonclassical states of light in cavity optomechanics

Cavity-optomechanics is an ideal platform for the generation non-Gaussian quantum states due to the anharmonic interaction between the light field and the mechanical oscillator; but exactly this interaction also impedes the preparation in pure states of the light field. In this paper we derive a driving protocol that helps to exploit the anharmonic interaction for state preparation, and that ensures that the state of the light field remains close-to-pure. This shall enable the deterministic preparation of photon Fock states or coherent superpositions thereof.

Symmetries of quantum evolutions

A cornerstone of quantum mechanics is the characterization of symmetries provided by Wigner's theorem. Wigner's theorem establishes that every symmetry of the quantum state space must be either a unitary transformation or an antiunitary transformation. Here we extend Wigner's theorem from quantum states to quantum evolutions, including both the deterministic evolution associated with the dynamics of closed systems and the stochastic evolutions associated with the outcomes of quantum measurements. We prove that every symmetry of the space of quantum evolutions can be decomposed into two state space symmetries that are either both unitary or both antiunitary. Building on this result, we show that it is impossible to extend the time-reversal symmetry of unitary quantum dynamics to a symmetry of the full set of quantum evolutions. Our no-go theorem implies that any time-symmetric formulation of quantum theory must either restrict the set of the allowed evolutions or modify the operational interpretation of quantum states and processes. Here we propose a time-symmetric formulation of quantum theory where the allowed quantum evolutions are restricted to a suitable set, which includes both unitary evolution and projective measurements but excludes the deterministic preparation of pure states. The standard operational formulation of quantum theory can be retrieved from this time-symmetric version by introducing an operation of conditioning on the outcomes of past experiments.

Deterministic preparation of W states via spin-photon interactions

Spin systems such as silicon or nitrogen vacancy centers in diamond, quantum dots and quantum dot molecules coupled to optical cavities appear as key elements for creating quantum networks as not only constituting the nodes of the network, but also assisting the creation of photonic networks. Here we study deterministic preparation of arbitrary size $W$ states with spin systems. We present an efficient operation on three qubits, two being the logical qubits and one being the ancillary qubit, where no interaction between the logical qubits are required. The proposed operation can create a $W$-type Einstein-Podolsky-Rosen (EPR) pair from two separable qubits, and expand that EPR pair or an arbitrary size $W$ state by one, creating a $W$-like state. Taking this operation as the fundamental building block, we show how to create a large scale $W$ state out of separable qubits, or double the size of a $W$ state. Based on this operation and focusing on nitrogen vacancy (NV) centers in diamond as an exemplary spin system, we propose a setup for preparing $W$ states of circularly polarized photons, assisted by a single spin qubit, where no photon-photon interactions are required. Next, we propose a setup for preparing $W$ states of spin qubits of spatially separated systems, assisted by a single photon. We also analyze the effects of possible imperfections in implementing the gates on the fidelity of the generated $W$ states. In our setups, neither post-measurement, nor post-processing on the states of spin or photonic qubit is required. Our setups can be implemented with current technology, and we anticipate that they contribute to quantum science and technologies.

Deterministic Controlled Remote Preparation of Two-qutrit Equatorial States

We present a novel scheme for deterministically realizing remote preparation of three-dimensional quantum states in a controlled manner. In this scheme, to link the three legitimate parties, generalized Einstein-Podolsky-Rosen (EPR) states, generalized Greenberger-Horne-Zeilinger (GHZ) states or their combinations are employed to product the shared quantum resources. Then to complete the deterministic controlled remote state preparation (DCRSP) in a three-dimensional system, some suitable sets of mutually orthogonal quantum states are hired as the measuring bases. It is shown that, after performing projective measurements under the proper measuring bases, the remote preparation of two-qutrit equatorial states can be successfully realized under control of a third party with unit successful probability.

Effect of Quantum Noise on Deterministic Remote Preparation of an Arbitrary Two-Qubit State With a Relay Node

We propose a scheme for deterministic remote preparation of an arbitrary two-qubit state via a relay node. Afterwards, we investigate how the scheme is influenced by the noise type, the initial state to be remotely prepared, and the decoherence rate. We find that the fidelity is symmetrical with the line (λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b-f</sub> =λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p-f</sub> =0.5) in bit-flip and phase-flip channels. In addition, the fidelity decreases with the increase of decoherence rate in the amplitude-damping and phase-damping channels. We also compare it with other RSP schemes. Since only Bell pairs work as the quantum channels, it makes our RSP scheme more available and feasible.

Effect of noise on deterministic remote preparation of an arbitrary two-qudit state by using a four-qudit χ-type state as the quantum channel

We present a protocol for remote preparation of an arbitrary two-qudit state by using a four-qudit [Formula: see text]-type state as the quantum channel via positive operator-valued measurement. We first propose the protocol for remote preparation of an arbitrary two-qudit state via positive operator-valued measurement in noiseless environment and then discuss the protocol in noisy environments. Four important quantum decoherence noise models, the dephasing noise, the qudit-flip noise, the qudit-phase-flip noise and the depolarizing noise, are considered in our protocol. The output states and the fidelities of remote state preparation in four different types of quantum noises are presented. It is shown the protocol for remote state preparation via positive operator-valued measurement with [Formula: see text]-type state has the advantage of transmitting less particles for remote preparing an arbitrary two-qudit state. The fidelities of remote state preparation depend on the coefficients of original two-qudit state and the decoherence rates of the noise models.

Deterministic bidirectional controlled remote preparation without information splitting

By using a five-qubit entangled state as the quantum channel, we propose an efficient protocol for implementing bidirectional controlled remote preparation of arbitrary single-qubit states with unit success probability. The senders do not need to perform information splitting and additional unitary operations due to the elaborately constructed measurement basis. Furthermore, three-bit classical communication can be saved at the controller’s broadcast channel with the aid of network coding. Then, we consider the effect of five-type noises on the proposed protocol. It is found that the fidelities of the output states are dependent on the coefficients of the prepared state and the noise parameter. Interestingly, the fidelity is irrelevant to the participators’ measurement results except in the amplitude-damping and phase-damping noises.

Assembled arrays of Rydberg-interacting atoms

Assembled arrays of individual atoms with Rydberg-mediated interactions provide a powerful platform for the simulation of many-body spin Hamiltonians as well as the implementation of universal gate-based quantum information processing. We demonstrate the first realization of Rydberg excitations and controlled interactions in microlens-generated multisite trap arrays of reconfigurable geometry. We utilize atom-by-atom assembly for the deterministic preparation of pre-defined 2D structures of rubidium Rydberg atoms with exactly known mutual separations and selectable interaction strength. By adapting the geometry and the addressed Rydberg state, a parameter regime spanning from weak interactions to strong coupling can be accessed. We characterize the simultaneous coherent excitation of non-interacting atom clusters for the state 57D5/2 and analyze the experimental parameters and limitations. For configurations optimized for Rydberg blockade utilizing the state 87D5/2, we observe collectively enhanced Rabi oscillations.

Bare-Excitation Ground State of a Spinless-Fermion-Boson Model and W-State Engineering in an Array of Superconducting Qubits and Resonators.

This Letter unravels an interesting property of a one-dimensional lattice model that describes a single itinerant spinless fermion (excitation) coupled to zero-dimensional (dispersionless) bosons through two different nonlocal coupling mechanisms. Namely, below a critical value of the effective excitation-boson coupling strength, the exact ground state of this model is the zero-quasimomentum Bloch state of a bare (i.e., completely undressed) excitation. It is demonstrated here how this last property of the lattice model under consideration can be exploited for a fast, deterministic preparation of multipartite W states in a readily realizable system of inductively coupled superconducting qubits and microwave resonators.

Efficient scheme for remote preparation of arbitrary n-qubit equatorial states

Recently, a scheme for deterministic remote preparation of arbitrary multi-qubit equatorial states was proposed by Wei et al. [Quantum Inf. Process. 17 70 (2018)]. It is worth mentioning that the construction of mutual orthogonal measurement basis plays a key role in quantum remote state preparation. In this paper, a simple and feasible remote preparation of arbitrary n-qubit equatorial states scheme is proposed. In our scheme, the success probability will reach unit. Moreover, there are no coefficient constraint and auxiliary qubits in this scheme. It means that the success probabilities are independent of the coefficients of the entangled channel. The advantage of our scheme is that the mutual orthogonal measurement basis is devised. To accomplish the quantum remote state preparation (RSP) schemes, some new sets of mutually orthogonal measurement basis are introduced.

Two Forms Schemes of Deterministic Remote State Preparation for Four-Qubit Cluster-Type State

Two deterministic schemes are put forward to preparing an arbitrary four-qubit cluster-type state remotely by using two Bell states as quantum channel. The coefficients of the prepared states can be not only real, but also complex. To accomplish the schemes, we introduce some novel sets of ingenious measurement basis vectors. Especially, for complex coefficients case, we give two different forms schemes. The receiver will reconstruct the initial state by means of some appropriate unitary operations. The outstanding advantage of the present schemes is that the success probability in all the considered remote state preparation (RSP) can reach 1.

Preparing Dicke States on a Quantum Computer

Exact requirement of controlled NOT (CNOT) and single-qubit gates to implement a quantum algorithm in a given architecture is one of the central problems in this computational paradigm. In this article, we take a tutorial approach in explaining the preparation of Dicke states $(\mathinner {|{D^n_k}\rangle })$ using concise realizations of partially defined unitary transformations. We show how to efficiently implement the state-of-the-art deterministic Dicke state preparation circuits and in turn optimize them in terms of CNOT and single-qubit gate counts. We explain theoretical ideas in reducing the gate counts and observe how these improvements are reflected in actual implementation of the circuits. To emphasize the advantages, we describe the circuit for preparing $\mathinner {|{D^4_2}\rangle }$ on the “ibmqx2” machine of the IBM quantum experience (QX) service. Our approach shows that the error induced due to noise in the system is lesser in comparison to the existing works. We conclude by describing the CNOT map of the generic $\mathinner {|{D^n_k}\rangle }$ preparation circuit and analyze different ways of distributing the CNOT gates in the circuit and its effect on the induced error in the Noisy Intermediate Scale Quantum environment.

Deterministic remote preparation of arbitrary single-qubit state via one intermediate node in noisy environment

We propose a remote state preparation scheme working in noisy environment via one intermediate node. Firstly, we report the remote preparation of an arbitrary single-qubit state with one intermediate node in ideal environment. Afterwards, we investigate the influence of four kinds of representative noises that are commonly encountered in practical applications of quantum communication protocols. Detailed analysis indicates that the fidelities of the output state rely on the coefficients of the prepared state and the decoherence rate. The turning point is λ=0.5 in both the bit-flip and phase-flip noisy channels. The fidelity in the depolarizing channel is related with the decoherence rate, and independent with the phase parameters.